'''simple docstring'''




def __lowerCAmelCase					(				UpperCamelCase__							)      ->       bool:
    if not isinstance(UpperCamelCase__							,    UpperCamelCase__							):
        raise ValueError('''Input series is not valid, valid series - [2, 4, 6]'''							)
    if len(UpperCamelCase__							) == 0:
        raise ValueError('''Input list must be a non empty list'''							)
    if len(UpperCamelCase__							) == 1:
        return True
    __lowerCamelCase            =    series[1] - series[0]
    for index in range(len(UpperCamelCase__							) - 1							):
        if series[index + 1] - series[index] != common_diff:
            return False
    return True






def __lowerCAmelCase					(				UpperCamelCase__							)      ->       float:
    if not isinstance(UpperCamelCase__							,    UpperCamelCase__							):
        raise ValueError('''Input series is not valid, valid series - [2, 4, 6]'''							)
    if len(UpperCamelCase__							) == 0:
        raise ValueError('''Input list must be a non empty list'''							)
    __lowerCamelCase            =    0
    for val in series:
        answer += val
    return answer / len(UpperCamelCase__							)


if __name__ == "__main__":
  import doctest

  doctest.testmod()

'''simple docstring'''




import numpy as np






def __lowerCAmelCase					(				UpperCamelCase__							,    UpperCamelCase__							,    UpperCamelCase__							,    UpperCamelCase__							,    UpperCamelCase__							)      ->       str:
    __lowerCamelCase            =    int(np.ceil((x_end - xa) / h							)							)
    __lowerCamelCase            =    np.zeros((n + 1,)							)
    __lowerCamelCase            =    ya
    __lowerCamelCase            =    xa

    for k in range(UpperCamelCase__							):
        __lowerCamelCase            =    f(UpperCamelCase__							,    y[k]							)
        __lowerCamelCase            =    f(x + 0.5 * h							,    y[k] + 0.5 * h * ka							)
        __lowerCamelCase            =    f(x + 0.5 * h							,    y[k] + 0.5 * h * ka							)
        __lowerCamelCase            =    f(x + h							,    y[k] + h * ka							)
        __lowerCamelCase            =    y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
        x += h

    return y


if __name__ == "__main__":
  import doctest

  doctest.testmod()
